According to The Sun, Tottenham head coach Mauricio Pochettino is interested in signing the 16-year-old.
The youngster scored 10 goals to help Nigeria win the Under-17 World Cup in Chile last month.
Osimhen is highly rated, but it seems that Spurs could lose him to their North London rivals Arsenal.
Another player Tottenham have been linked with is Paris Saint-Germain midfielder Adrien Rabiot.
According to a report in The Independent earlier this month, Spurs are interested in signing the 20-year-old in the January transfer window.
The Sun has claimed that Arsenal manager Arsene Wenger wants to sign the France Under-21 international due to injuries to Jack Wilshere and Francis Coquelin.
However, it seems that Rabiot will remain at French champions PSG for the rest of the season.
“My dream is that he (Rabiot) might become captain of PSG one day,” PSG president Nasser Al-Khelaifi has told Le Figaro, as translated by ESPN. “But he has to respect the club, the coach and his teammates.
"He's part of the PSG family and he should respect it. He understood the message. He'll be there at 100 per cent in January.”
Rabiot has created four chances in 13 Ligue 1 appearances for PSG so far this season. The youngster has scored one goal and created two chances in three Champions League games.